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Newtons method for multiple nonlinear equations

Again we use a Taylor series expansion to obtain Newton s method, representing the fth function in the vicinity of the current estimate as [Pg.72]

Assuming that is sufficiently close to the true solution Xs that we introduce little error by dropping the terms of quadratic and higher order, [Pg.73]

For convenience, we collect the first partial derivatives into the A x A Jacobian matrix jl l = with elements [Pg.73]

The truncated Taylor series expansion then becomes [Pg.73]

We thus generate the new estimate of the solution, Xs by solving the set of linear algebraic equations [Pg.73]




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